Problem: $\text A = \left[\begin{array}{rr}2 & 3 \\ 4 & -2\end{array}\right]$ What is the determinant of $\text A$ ?
The determinant of a 2x2 matrix can be computed the following way: $ \left|\begin{array}{rr}a & b \\ c & d\end{array}\right| = (a \times d)-(b \times c) $ In this specific case, $ \left|\begin{array}{rr}2 & 3 \\ 4 & -2\end{array}\right| = (2 \cdot -2)-(3 \cdot 4) $ $ = -16 $